Method and apparatus for indirect determination of shear velocity from guided modes

Abstract

Methods and apparatus are described for estimating shear wave slowness of formations traversed by a borehole from guided wave acoustic log data. Acoustic energy is generated at a point in the borehole and received at at least four receiver stations spaced one from the other and from the generating point. Full wave forms of the received signals are produced and windowed to identify guided wavelets. Fourier transforms of the guided wavelets are obtained and from these determined the phase velocity and frequency of the guided wavelet. Values of formation density, drilling fluid density, drilling fluid slowness and borehole diameter are measured and a value of Poissons ratio may be estimated. A multi-dimensional matrix is established comprised of predetermined ranges of assumed values of frequency, Poissons ratio, drilling fluid slowness, drilling fluid density, formation density, phase velocity and borehole diameter. The measured data is fitted to the multi-dimensional matrix to obtain an estimate of shear wave slowness at the point in the borehole, and the estimate is recorded as a function of depth.

What is claimed is: 
     
       1. A method of estimating shear wave slowness of formations traversed by a borehole from acoustic log data including guided wave comprising the steps of: generating acoustic energy at a point in the borehole,   receiving that acoustic energy as acoustic signals in the form of full waveforms, which include as a portion thereof waveforms representing guided waves, at each of at least four receiver stations spaced one from the other and from the point at which said acoustic energy was generated,   windowing each of said full waveforms to identify those portions representing a guided wave,   determining the phase velocity and frequency of the guided wave from that portion of the full waveform representing the guided wave,   measuring the values for formation density, drilling fluid density, drilling fluid slowness, borehole diameter, and Poisson's ratio,   establishing a multi-dimensional matrix comprised of given ranges of assumed values of guided wave frequency, Poisson's ratio, drilling fluid slowness, drilling fluid density, formation density, guided wave phase velocity and borehole diameter,   fitting the measured values to the multi-dimensional matrix to obtain an estimate of shear wave slowness at that point in the borehole, and   recording the estimate as a function of depth.   
     
     
       2. The method of claim 1 wherein the acoustic energy is received at eight receiver locations and four wave forms are selected exhibiting low orders of interference of the guided wave component. 
     
     
       3. The method of claim 1 wherein the guided wave is the Stoneley wave. 
     
     
       4. The method of claim 1 wherein the guided wave is the first reflected mode. 
     
     
       5. The method of claim 1 wherein the step of measuring drilling fluid slowness is conducted in situ during the course of producing full wave forms of the acoustic signals. 
     
     
       6. The method of claim 1 wherein the establishment of said matrix includes the generation for the assumed values of poles at zero points in f-k space. 
     
     
       7. The method of claim 6 wherein the determination of poles involves the solution of a two-dimensional transfer function   A(k.sub.z,w)     where   k z  is wave number, and   w is angular frequency.   
     
     
       8. The method of claim 1 wherein the fitting of values is accomplished by way of a multilevel interpolation, to obtain at each level a solution of shear modulus index with a final unique value of shear modulus index produced at the final level. 
     
     
       9. The method of claim 1 in which the fitting of values generates a unique value of shear modulus and the value of shear wave slowness is computed in accordance with the expression ##EQU3## where 1/β 2  is the shear wave slowness α 1  is the velocity of the drilling fluid,   μ 2  /λ 1  is the shear modulus,   ρ 2  is the formation density, and   ρ 1  is the drilling fluid density.   
     
     
       10. The method of claim 8 wherein the first step of the multilevel interpolation utilizes the measured value of guided wave phase velocity and a non-linear function relating phase velocity and shear modulus. 
     
     
       11. The method of claim 10 wherein the second step of the multilevel interpolation utilizes the measured value of frequency and a non-linear function relating frequency and shear modulus for fixed values of borehole size, Poisson's ratio, and the ratio of formation density to drilling fluid density. 
     
     
       12. A method of acoustic logging a formation to determine whether the formation exhibits isotropic or traversely isotropic characteristics comprising the steps of measuring the shear wave velocity traversing the formation,   estimating the shear wave velocity of the formation from Stoneley wave phase slowness, and   comparing the measured value of shear wave velocity with the estimated value of shear wave velocity to indicate the isotropic nature of the formation.   
     
     
       13. A system for estimating shear wave slowness of formations traversed by a borehole from acoutstic log data including guided waves comprising: a sonde having means for generating acoustic energy at a point in the borehole and means for receiving acoustic energy as acoustic signals in the form of full waveforms, which include as a portion thereof waveforms representing guided waves, at each of at least four receiver stations spaced one from the other and from the generating point,   means for windowing each of said full waveforms to identify those portions representing a guided wave,   means for determining the phase velocity and frequency of the guided wave from that portion of the full waveform representing the guided wave,   means for measuring the values for formation density, drilling fluid density, drilling fluid slowness, borehole diameter, and Poisson's ratio,   means for obtaining a value of Poisson's ratio, means for establishing a multi-dimensional matrix comprised of given ranges of assumed values of guided wave frequency, Poisson's ratio, drilling fluid slowness, drilling fluid density, formation density, guided wave phase velocity and borehole diameter, and   means for fitting the measured values and the value of Poisson's ratio to the multi-dimensional matrix to obtain an estimate of shear wave slowness at that point in the borehole.   
     
     
       14. The system of claim 13 wherein said means for measuring drilling fluid slowness comprises: a cavity in the side of said sonde   a transmitter of acoustic energy and a receiver of acoustic energy located in said cavity and spaced one from the other,   means adjacent said cavity for permitting ingress to and egress from said cavity of drilling fluid as the sonde is moved along the borehole whereby drilling fluid fills said cavity between said transmitter and said receiver, and   means responsive to the time occurrence of acoustic energy at said transmitter and receiver for measuring the travel time of acoustic energy through the drilling fluid.   
     
     
       15. In an acoustic logging system comprising a sonde for logging formations traversed by a borehole filled with drilling mud and having a plurality of acoustic transducers including at least one acoustic transmitter and at least two acoustic receivers spaced from one another and from said transmitter along the length of said sonde, means for measuring the travel time of acoustic energy through the drilling mud comprising: a cavity in the side of said sonde,   a transmitter of acoustic energy and a receiver of acoustic energy located in said cavity and spaced one from the other,   means adjacent said cavity for permitting ingress to and egress from said cavity of drilling mud as the sonde is moved along the borehole whereby drilling mud fills said cavity between said transmitter and said receiver, and   means responsive to the time occurrence of acoustic energy at said transmitter and receiver for measuring the travel time of acoustic energy through the drilling mud.   
     
     
       16. Apparatus for determining an isotropic characteristic of underground formations surrounding a borehole filled with fluids comprising: a support member,   first means, mounted on said support member for measuring sonic wave train propagation in underground formations surrounding said borehole,   second means, mounted on said support member, for measuring sonic wave train propagation in the fluids contained within said borehole,   means for effecting signal filtering to distinguish components of the sonic wave train measured by said first means, said filtering means having as an input the output of said second measuring means, and   means for deriving said isotropic characteristic of the formations from said distinguished components.   
     
     
       17. A method for determining isotropic characteristics of underground formations surrounding a borehole filled with fluids comprising the steps of: measuring sonic wave train propagation in underground formations surrounding said borehole at a given depth of the borehole,   simultaneously measuring sonic wave train propagation in the fluids contained within said borehole at said given depth of the borehole,   filtering the sonic wave train measured in the underground formation surrounding the borehole from the sonic wave train measured in the fluid contained in the borehole, to distinguish components of the sonic wave train and   using the filtered components to derive said isotropic characteristics of the formations.